On non-degenerate singular points of normalized Ricci flows on some generalized Wallach spaces

Abstract

The present paper devoted to problems of Riemannian geometry and planar dynamical systems. In particular we study non-degenerate singular points of normalized Ricci flows on special type of generalized Wallach spaces. Our main goal is to prove the absence of such points. The main idea is based on a special set Ω introduced in [1, 2] for studying general properties of degenerate singular points of Ricci flows. More concretely, for solving the mentioned problem we use the facts that the set ( 0,1 / 2)3 ᴖΩ is connected and the set ( 0,1 / 2)3\Ω consists of three connected components as it was proved in [3].